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A Directionally Varying Change Points Model for Quantifying the Impact of a Point Source


Point sources in spatially referenced data can impact outcomes in surrounding locations (e.g., a factory that emits air pollution). Previous statistical methods have sought to describe the non-stationary correlation induced by the presence of a point source, with fewer attempting to quantify its overall impact. We introduce directionally varying change points (DVCP), a model that aims to estimate the magnitude of the impact of a point source as well as its range of influence across the spatial domain. DVCP allows for a unique change point parameter, describing the range of influence of a point source, at every angle extending from the source and uses a Gaussian process with directionally defined correlation function to facilitate estimation of the parameters. The Gaussian predictive process approximation is used for fitting the model to large datasets. Through simulation, we show that DVCP can easily accommodate a wide range of shapes defining the range of influence. We apply DVCP to better understand spatial patterns of ambient PM\(_{2.5}\) concentrations and issues related to environmental inequity in California and Colorado. The method is available in the R package DVCP.

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Correspondence to Joshua L. Warren.

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Song, J., Warren, J.L. A Directionally Varying Change Points Model for Quantifying the Impact of a Point Source. JABES 27, 46–62 (2022).

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  • Bayesian modeling
  • Environmental inequity
  • Gaussian process
  • Spatial analysis